There is no dedicated nightlife/restaurant area in Asuncion or around the Sheraton.
The city has become pretty dynamic in this and other regards over the last couple of years. You will need a car or taxi to move around, even for shorter distances except for Shopping del Sol across the street which offers a decent food court and a few restos (nothing to rave about), Parilla "Entrecote" opposite the hotel entrance (okish grill), Italian ristorante "Periglia" (or so) also opposite and perhaps a nice Parilla a few blocks away on Sta. Theresa to the right called La Cabrita.
If looking for a nice place by taxi I can of course recommend the restaurant of my cousin called "La Esquadra" 10 min away by car . Excellent homebrew beer German style and good beef or pizza.
Just checked out of this Sheraton today and have to say they have become very good. Room standard, staff attention, Platinum handling - you name it.